Question

The rate of change of function f(x) = 3x⁵ – 5x³ + 5x – 7 is minimum when x is 

(a) 0 

(b) (1/√2) 

(c) √2 

(d) ± (1/√2)

Answer 1

The correct option (d) ± (1 /√2)   

Explanation:

Let v is rate of change of given function

∴ v = f'(x) = 15x⁴ – 15x² + 5

∴ (dv/dx) = 60x³ – 30x

[(d²v)/(dx²)] = 180x² – 30

∴ (dv/dx) = 0 ⇒ 60x² – 30x = 0

∴ x = ± (1/√2), 0

at x = 0, [(d²v)/(dx²)] = – 30 < 0

at x = ± (1/√2), [(d²v)/(dx²)] = 60 > 0

∴ v is minimum at x = ± (1/√2)